Optimizing a Linearly Constrained Quadratic Programming Problem Using Eigen-Value Decomposition and Resultant Vector Ascent Method

This paper suggests an iterative method for optimizing a Quadratic Programming Problem, constrained with a set of Linear Inequalities (less than type), regardless of the nature of the square matrix ( B ) within the objective function. To reach the global solution the entire travel is devised with a...

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Bibliographic Details
Published in:International journal of applied and computational mathematics Vol. 11; no. 6; p. 231
Main Author: Sarkar, Subhadip
Format: Journal Article
Language:English
Published: New Delhi Springer India 01.12.2025
Springer Nature B.V
Subjects:
Applications of Mathematics
Approximation
Computational Science and Engineering
Constraints
Eigenvalues
Eigenvectors
Iterative methods
Linear functions
Literature reviews
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Methods
Nuclear Energy
Operations Research/Decision Theory
Optimization
Original Paper
Production planning
Quadratic programming
Resultants
Slack variables
Theoretical
Variables
Global optimal solution
Resultant Vector Ascent Method
Quadratic Programming
Null space
Eigen Value Decomposition
ISSN:2349-5103, 2199-5796
Online Access:Get full text
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Summary:This paper suggests an iterative method for optimizing a Quadratic Programming Problem, constrained with a set of Linear Inequalities (less than type), regardless of the nature of the square matrix ( B ) within the objective function. To reach the global solution the entire travel is devised with a set of specially designed ( n – m ) (>  m ) vectors while incorporating a Resultant Vector Ascent Method (where  n  and  m represent the number of variables (including slack variables) and constraints). These vectors are located in the null space of the constraint matrix and half of them are dependent on the Eigenvectors of B . The prescribed movements can optimize the problem with a time complexity of and without causing a looping problem during degeneracy .
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ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-025-02048-9